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GREENSBORO, N.C. - Despite a competitive economy in which success increasingly depends on obtaining a college degree, one in four students in this country does not even finish high school in the usual four years.

Matthew Kelly was in danger of becoming one of them.

Tests showed he had a high intellect, but Kelly skipped homework and was barely passing some of his classes in his early years of high school. He was living in a motel part of the time and both his parents were out of work. His mother, a former nurse, feared that Matthew had so little interest he would drop out without graduating.

Then his guidance counselor suggested he take some courses at a nearby vocational academy for his junior year. For the first time, the teenager excelled, earning A’s and B’s in subjects like auto repair, electronics and metals technology. “When it comes to practicality, I can do stuff really well,’’ said Kelly, now 19.

So well, that he has earned a scholarship to attend a community college this fall. He even talks of pursuing a bachelor’s degree in engineering some day, and opening his own business.

Now, federal funding to provide such vocational and technical education is at risk. President Obama has instead made it a priority to raise overall academic standards and college graduation rates, and aims to shrink the small amount of federal spending for vocational training in public high schools and community colleges. That aid comes primarily in the form of Perkins grants to states.

The administration has proposed a 20-percent reduction in its fiscal 2012 budget for career and technical education, to a little more than $1 billion, even as it seeks to increase overall education funding by 11 percent.

The only real alternative to public schools for career training is profit-making colleges and trade schools, many of which have been criticized for sending students deeply into debt without improving their job prospects. A little more than 1 in 10 students in higher education attend a profit-making institution.

Proponents of career education in public high schools and community colleges point to apparent successes like Kelly and other research to demonstrate that their courses serve a group of students at most risk of being left behind. Without high school, much less college, many young people - particularly men and members of minority groups - end up doing low-skill work, relying on their youth and brawn. Those types of jobs were slashed during the downturn.

Recognizing that employment and income have expanded for those with college degrees, the president has said he wants America to produce the highest proportion of college graduates in the world by 2020.

Last year, fewer than a third of all 25- to 29-year-olds in the United States had earned a bachelor’s degree or higher.